There were two passenger lists (Hamburg to Glasgow and Glasgow to New York) and the Siegel families were grouped differently on the two lists. This helped a little bit in tracking the family units after they reached America.

Using a strategy of searching for children when unsure of the parents' names, I searched for Lena Segal and found the family in the 1900 U.S. Census in Dennis Township, in the section which in 1903 became the Borough of Woodbine.

This census lists the family as Samuel, born in August 1843, Bertha (not Blume or Rebecca), born in March 1874. (The passenger lists have him as born in 1835 and her as born in 1865.) They had been married for ten years and had a daughter, Lena, born in August 1890, and a son, Louis, born in May 1898. They were all born in Russia, except Louis, who was born in New Jersey. This census records (correctly) that Samuel immigrated in 1891 and was a naturalized citizen.

His occupation in Woodbine in 1900 was butcher.

By 1910, he and his family were about 23 miles away in Holly Beach, Cape May, New Jersey, which Wikipedia tells me was a borough from 1885 until January 1, 1912, when it became a part of Wildwood. In Holly Beach in 1910, he was a Junk Peddler. My mother-in-law remembers the family as always being in Wildwood.